# Formation of asset allocation inputs (Week 4) Flashcards

Modern Portfolio theory assume

All investors have same expectation of asset returns.

Assumed the asset returns are Identically and independently distributed. All market portfolio they have the same probability distribution. (return generation process is stable for one asset do not accommodate changes for risky assets)

Forming asset assumptions

- Asset Assumptions: return, variance, covariance
- Start from objectives (ALWAYS!): link client objectives to the data assumptions, e.g. data interval, sample period, etc.
- Lots of choices to make

What does “forming asset assumptions” mean in asset allocation?

A

Forecast asset expected returns.

B

Forecast covariance of all aset classes in the portfolio.

D

Forecast standard deviation for all assets in the portfolio.

Quantitative analysis using historical returns is non-trivial part of the asset allocation process.

Select all of the correct statements about data selection in portfolio analysis

B Data selection has to be linked to investor’s objectives and investment horizon.

C

It’s more likely to capture the entire distribution with longer data period, but it’s also more likely to include structural changes, i.e. some data in the past maybe not relevant for the forecast period.

F

It’s ultimately a trade-off. Longer data intervals may mitigate the data problem as a result of thin trading or appraisal based valuations, but you end up with less data points in short period of time.

Slide 3

To forecast the expected returns of a group of assets, which methods below are appropriate?

Implied views method that let the model generate expected returns conditional on the variance-covariance metrics so that a user-specified portfolio (e.g. the benchmark) is the optimal portfolio on the efficient frontier.

C

Bayesian technique, for instance, James Stein estimator.

D

Black-Litterman approach that combines market equibrium and investor’s expectations.

Confidence interval around per-annum expected return

usually narrows with investment horizon.

as “variance” or “risk” in a general sense is spread over more periods with longer investment horizon when it’s measured on per-period or per-annum returns. Over long term, returns tend to converge to mean. Variance tends to reduce with investment horizon.

Confidence interval around wealth can

either widen or narrow with investment horizon.

wealth is an accumulation of all of the returns in each period over the entire investment horizon. Depending on how these period returns are correlated, confidence interval around wealth may widen or narrow with investment horizon

Assume a return series demonstrates significant positive serial correlation. Which of the following statements is likely to be correct under this situation?

B

Variance of per annum returns tends to decrease with investment horizon.

C

Variance of wealth tends to increase with investment horizon.

D

Variance of per annum returns tends to increase with investment horizon.

E

The underlying asset may be thinly-traded.

Variance of wealth tends to

When a return series demonstrates significant positive serial correlation, it’s most likely variance of wealth tends to increase with investment horizon because the “momentum” builds up over multiple periods over the investment horizon. The longer the investment horizon, the more “momentum” is incorporated in wealth which is (1+Rt1)(1+Rt2)…. Variance of per annum or per-period returns may increase or decrease over longer investment horizon even though significant positive serial correlation presents as they are measured in per period term

Data selection in portfolio analysis

- has to be linked to investor’s objectives and investment horizon. align data period with investment horizon. in practice, have longer investment horizon than data period

benefit and disadvantage of longer data period

- capture the entire distribution
- include structural changes e.g. some data in the past may not be relevant for the forecast period

Choosing daily and weekly data

is problematic due to high serial correlation. most quantitative measure of risk assumes the returns are independent.

monthly or quarterly should be preferred

When do you exclude an outlier

no chance of this negative market event happening at all.

may reduce the impact of these but do not delete the outliers from time series

Longer data interval trade off

mitigate the data problem as a result of thin trading and appraisal based valuations

but you end up with less data points in a short period of time

when do you use historical mean of each asset class to forecast expected returns of a group of assets

never, unless you have 100 years of data

but even if you do, you would be including a lot of unrelated info

mean variance optimisation has been described as

an unreliable method and optmisers have been error maximisers

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

DP

Direct property is being influenced by appraisal valuations. This reduces measures of volatility at shorter horizons. The 3-year and 5-year standard deviations of about 11% are probably more representative of ‘true’ underlying volatility. Also note the large serial correlation for DP at quarterly intervals (0.80). This probably reflects a rolling quarterly revaluation cycle

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

DP

Direct property is being influenced by appraisal valuations. This reduces measures of volatility at shorter horizons. The 3-year and 5-year standard deviations of about 11% are probably more representative of ‘true’ underlying volatility. Also note the large serial correlation for DP at quarterly intervals (0.80). This probably reflects a rolling quarterly revaluation cycle

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

3

AE has a complex serial correlation pattern, which is slightly positive at monthly and quarterly intervals, but negative at yearly intervals. Its standard deviation is stable up to 1-year, before decreasing.

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

2

Standard deviation of AC approaches then exceeds AFI and WFI as investment horizon increases. This reflects combination of high positive serial correlation (when cash rates start moving, they tend to keep going), plus fact that cash investments are ‘rolled over’ and hence ‘re-priced’

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

For series with higher serial correlation, standard deviation tends to increase with investment horizon. Examples include WE, DP, AFI. WFI and (especially) AC.

**correlation**

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 4

Correlations also tend to be lower over shorter horizons as short-term data is ‘noisier’, and hence can hide any underlying correlation structure. The latter begins to show through the noise as the measurement interval is lengthened.

**correlation**

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 3

Over the longer term, all assets reflect the impact of common influences such as:

(a) broader economic and market trends, and

(b) realization of (positive) expected returns over the passage of time. This influences show up as a rise in correlation with holding period.

**correlation**

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 2

DP returns reflect irregular appraisal valuations, which react gradually to market developments. This creates the appearance of no correlation with AE and LP at shorter horizons, as they react immediately to market developments.

**correlation**

Reason 1

AE and LP are both listed, and hence commonly reflect broader equity market fluctuations.

Std

correlation

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

3.

Prevalence of serial correlation and/or measurement lags

n the data should be considered, e.g. thin-trading, appraisals. Lengthening the measurement interval will dilute the impact. The relevance of this issue can relate to the type of assets being analyzed (e.g. liquidity, valuation method)

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

2.

Finer data means more data points. This is useful if there is a requirement to restrict the time period from which the data is drawn in order to generate ‘fresh’ estimates of risk measures such as standard deviation and covariance.

An example would be if there has been a structural change so that older data becomes less relevant. Estimates can be drawn from the recent part of the available history by cutting the data into finer intervals (e.g. monthly instead of annually)

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

1.

Ideally align measurement interval with investment time horizon (or ‘review’ period) if practical.

Considerations in selecting measurement period

- Availability of data – this constrains what choice of period you have
- Which period is most representative looking forward – Is the period long enough to capture all relevant events? Or could older data be misleading to instabilities such as structural change, etc?
- Whether any instability can be successfully modeled – If so, a longer period may still be preferable to estimate the model

Causes of instability in the series plotted

Std dev of WE

fluctuations in series for hedged WE largely reflects positioning of ‘crashes’ such as 1987, tech wreck and GFC

− difference between hedged and unhedged series reflects impact of currency, and the (changing) role of A$ as a ‘risk’ asset that is highly correlated with global equities – at least until recently